Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory

We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.Comment: Final version as accepted for publication in Phys. Rev. B (4 pages, 3 figures

Dynamical typicality of quantum expectation values

We show that the vast majority of all pure states featuring a common expectation value of some generic observable at a given time will yield very similar expectation values of the same observable at any later time. This is meant to apply to Schroedinger type dynamics in high dimensional Hilbert spaces. As a consequence individual dynamics of expectation values are then typically well described by the ensemble average. Our approach is based on the Hilbert space average method. We support the analytical investigations with numerics obtained by exact diagonalization of the full time-dependent Schroedinger equation for some pertinent, abstract Hamiltonian model. Furthermore, we discuss the implications on the applicability of projection operator methods with respect to initial states, as well as on irreversibility in general.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let

The TWINS exospheric neutral H-density distribution under solar minimum conditions

Terrestrial exospheric atomic hydrogen (H) resonantly scatters solar Lyman-α (121.567 nm) radiation, observed as the glow of the H-geocorona. The Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) satellites are equiped with two Lyman-α line-of-sight Detectors (LADs) each. Since during the past solar minimum conditions the relevant solar control parameters practically did not vary, we are using LAD data between June and September 2008 to create a time averaged hydrogen geocorona model representative for these solar minimum conditions. In this averaged model we assume that the H-geocorona is longitudinally symmetric with respect to the earth-sun line. We find a 3-dimensional H-density distribution in the range from 3 to 8 earth radii which with some caution can also be extrapolated to larger distances. For lower geocentric distances than 3 earth radii a best fitting r-dependent Chamberlain (1963)-like model is adapted. Main findings are larger than conventionally expected H-densities at heights above 5 <I>R</I>_E and a pronounced day-to-night side H-density asymmetry. The H-geocorona presented here should serve as a reference H-atmosphere for the earth during solar minimum conditions

Spin anisotropy effects in dimer single molecule magnets

We present a model of equal spin $s_1$ dimer single molecule magnets. The spins within each dimer interact via the Heisenberg and the most general set of four quadratic anisotropic spin interactions with respective strengths $J$ and $\{J_j\}$, and with the magnetic induction ${\bf B}$. We solve the model exactly for $s_1=1/2, 1, 5/2$, and for antiferromagnetic Heisenberg couplings ($J<0$), present ${\bf M}({\bf B})$ curves at low $T$ for these cases. Low-$T$ $C_V({\bf B})$ curves for $s_1=1/2$ and electron paramagnetic susceptibility $\chi({\bf B},\omega)$ for $s_1=1$ are also provided. For weak anisotropy interactions, we employ a perturbative treatment, and show that the Hartree and extended Hartree approximations lead to reliable analytic results at low $T$ and large $B$ for these quantities and for the inelastic neutron scattering cross-section $S({\bf B}, {\bf q},\omega)$. Our results are discussed with regard to existing ${\bf M}({\bf B})$ experiments on $s_1=5/2$ Fe$_2$ dimer single molecule magnets, and suggest that one of them contains a substantial amount of single-ion anisotropy, without any sizeable global spin anisotropy. We urge further experiments of the above types on single crystals of Fe$_2$ and on some $s_=9/2$ [Mn$_4$]$_2$ dimers, in order to elucidate the precise values of the various microscopic interactions.Comment: 30 pages, 25 figures, submitted to Phys. Rev.

Dynamics of non-equilibrium membrane bud formation

The dynamical response of a lipid membrane to a local perturbation of its molecular symmetry is investigated theoretically. A density asymmetry between the two membrane leaflets is predominantly released by in-plane lipid diffusion or membrane curvature, depending upon the spatial extent of the perturbation. It may result in the formation of non-equilibrium structures (buds), for which a dynamical size selection is observed. A preferred size in the micrometer range is predicted, as a signature of the crossover between membrane and solvent dominated dynamical membrane response.Comment: 7 pages 3 figure

Possible potentials responsible for stable circular relativistic orbits

Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In the present article an attempt has been made to generalize Bertrand's theorem to the central force problem of relativistic systems. The stability criterion for potentials which can produce stable, circular orbits in the relativistic central force problem has been deduced and a general solution of it is presented in the article. It is seen that the inverse square law passes the relativistic test but the kind of force required for simple harmonic motion does not. Special relativistic effects do not allow stable, circular orbits in presence of a force which is proportional to the negative of the displacement of the particle from the potential center.Comment: 11 pages, Latex fil

Observations of oxidation products above a forest imply biogenic emissions of very reactive compounds

International audienceVertical gradients of mixing ratios of volatile organic compounds have been measured in a Ponderosa pine forest in Central California (38.90° N, 120.63° W, 1315m). These measurements reveal large quantities of previously unreported oxidation products of short lived biogenic precursors. The emission of biogenic precursors must be in the range of 13-66µmol m-2h-1 to produce the observed oxidation products. That is 6-30 times the emissions of total monoterpenes observed above the forest canopy on a molar basis. These reactive precursors constitute a large fraction of biogenic emissions at this site, and are not included in current emission inventories. When oxidized by ozone they should efficiently produce secondary aerosol and hydroxyl radicals

Observations of oxidation products above a forest imply biogenic emissions of very reactive compounds

International audienceMeasurements of volatile organic compounds in a pine forest (Central California, 38.90° N, 120.63° W, 1315 m) reveal large quantities of previously unreported oxidation products of short lived biogenic precursors. The emission of biogenic precursors must be in the range of 13?66 µmol m?2 h?1 to produce the observed oxidation products. That is 6?30 times the emissions of total monoterpenes observed above the forest canopy on a molar basis. These reactive precursors constitute the largest fraction of biogenic emissions at this site, and are not included in current emission inventories. When oxidized by ozone they should efficiently produce secondary aerosol and hydroxyl radicals

A Group-Based Yule Model for Bipartite Author-Paper Networks

This paper presents a novel model for author-paper networks, which is based on the assumption that authors are organized into groups and that, for each research topic, the number of papers published by a group is based on a success-breeds-success model. Collaboration between groups is modeled as random invitations from a group to an outside member. To analyze the model, a number of different metrics that can be obtained in author-paper networks were extracted. A simulation example shows that this model can effectively mimic the behavior of a real-world author-paper network, extracted from a collection of 900 journal papers in the field of complex networks.Comment: 13 pages (preprint format), 7 figure

Maladaptation and the paradox of robustness in evolution

Background. Organisms use a variety of mechanisms to protect themselves against perturbations. For example, repair mechanisms fix damage, feedback loops keep homeostatic systems at their setpoints, and biochemical filters distinguish signal from noise. Such buffering mechanisms are often discussed in terms of robustness, which may be measured by reduced sensitivity of performance to perturbations. Methodology/Principal Findings. I use a mathematical model to analyze the evolutionary dynamics of robustness in order to understand aspects of organismal design by natural selection. I focus on two characters: one character performs an adaptive task; the other character buffers the performance of the first character against perturbations. Increased perturbations favor enhanced buffering and robustness, which in turn decreases sensitivity and reduces the intensity of natural selection on the adaptive character. Reduced selective pressure on the adaptive character often leads to a less costly, lower performance trait. Conclusions/Significance. The paradox of robustness arises from evolutionary dynamics: enhanced robustness causes an evolutionary reduction in the adaptive performance of the target character, leading to a degree of maladaptation compared to what could be achieved by natural selection in the absence of robustness mechanisms. Over evolutionary time, buffering traits may become layered on top of each other, while the underlying adaptive traits become replaced by cheaper, lower performance components. The paradox of robustness has widespread implications for understanding organismal design